Diversity of reproduction rate supports cooperation in the prisoner's dilemma game on complex networks

Abstract. In human societies the probability of strategy adoption from a given person may be affected by the personal features. Now we investigate how an artificially imposed restricted ability to reproduce, overruling ones fitness, affects an evolutionary process. For this purpose we employ the evolutionary prisoner's dilemma game on different complex graphs. Reproduction restrictions can have a facilitative effect on the evolution of cooperation that sets in irrespective of particularities of the interaction network. Indeed, an appropriate fraction of less fertile individuals may lead to full supremacy of cooperators where otherwise defection would be widespread. By studying cooperation levels within the group of individuals having full reproduction capabilities, we reveal that the recent mechanism for the promotion of cooperation is conceptually similar to the one reported previously for scale-free networks. Our results suggest that the diversity in the reproduction capability, related to inherently different attitudes of individuals, can enforce the emergence of cooperative behavior among selfish competitors.

[1]  G. Szabó,et al.  Evolutionary games on graphs , 2006, cond-mat/0607344.

[2]  Xiang Li,et al.  Roles of mixing patterns in cooperation on a scale-free networked game. , 2007, Physical review. E, Statistical, nonlinear, and soft matter physics.

[3]  K. Lindgren,et al.  Evolutionary dynamics of spatial games , 1994 .

[4]  F. C. Santos,et al.  Graph topology plays a determinant role in the evolution of cooperation , 2006, Proceedings of the Royal Society B: Biological Sciences.

[5]  Arne Traulsen,et al.  Coevolution of strategy and structure in complex networks with dynamical linking. , 2006, Physical review letters.

[6]  Zhi-Xi Wu,et al.  Evolutionary prisoner's dilemma game with dynamic preferential selection. , 2005, Physical review. E, Statistical, nonlinear, and soft matter physics.

[7]  Attila Szolnoki,et al.  Rock-scissors-paper game on regular small-world networks , 2004 .

[8]  Albert,et al.  Emergence of scaling in random networks , 1999, Science.

[9]  B. M. Fulk.  MATH , 1992 .

[10]  R. Rosenfeld.  Nature , 2009, Otolaryngology--head and neck surgery : official journal of American Academy of Otolaryngology-Head and Neck Surgery.

[11]  J. J. Arenzon,et al.  Does mobility decrease cooperation? , 2006, Journal of theoretical biology.

[12]  M. Nowak.  Five Rules for the Evolution of Cooperation , 2006, Science.

[13]  M. Nowak,et al.  MORE SPATIAL GAMES , 1994 .

[14]  Zhi-Xi Wu,et al.  Evolutionary prisoner's dilemma game on BarabsiAlbert scale-free networks , 2007 .

[15]  Wang Ying-Hai,et al.  Prisoner's Dilemma Game with Heterogeneous Influential Effect on Regular Small-World Networks , 2006 .

[16]  Martin A Nowak,et al.  Evolutionary graph theory: breaking the symmetry between interaction and replacement. , 2007, Journal of theoretical biology.

[17]  M. Perc,et al.  Social diversity and promotion of cooperation in the spatial prisoner's dilemma game. , 2007, Physical review. E, Statistical, nonlinear, and soft matter physics.

[18]  György Szabó,et al.  Phase transitions and volunteering in spatial public goods games. , 2002, Physical review letters.

[19]  W. Hamilton,et al.  The Evolution of Cooperation , 1984 .

[20]  Bing-Hong Wang,et al.  Emergence of cooperation induced by preferential learning , 2006 .

[21]  Changshui Zhang,et al.  Learning and Innovative Elements of Strategy Adoption Rules Expand Cooperative Network Topologies , 2007, PloS one.

[22]  Angel Sánchez,et al.  Altruism may arise from individual selection. , 2004, Journal of theoretical biology.

[23]  M. Nowak,et al.  Evolutionary games and spatial chaos , 1992, Nature.

[24]  M. Kuperman,et al.  Social games in a social network. , 2000, Physical review. E, Statistical, nonlinear, and soft matter physics.

[25]  N. Masuda.  Participation costs dismiss the advantage of heterogeneous networks in evolution of cooperation , 2007, Proceedings of the Royal Society B: Biological Sciences.

[26]  G. Szabó,et al.  Phase diagrams for an evolutionary prisoner's dilemma game on two-dimensional lattices. , 2005, Physical review. E, Statistical, nonlinear, and soft matter physics.

[27]  G. Szabó,et al.  Cooperation enhanced by inhomogeneous activity of teaching for evolutionary Prisoner's Dilemma games , 2006, q-bio/0610001.

[28]  K. Sigmund,et al.  The efficiency of adapting aspiration levels , 1998, Proceedings of the Royal Society of London. Series B: Biological Sciences.

[29]  M. Perc.  Transition from Gaussian to Levy distributions of stochastic payoff variations in the spatial prisoner's dilemma game. , 2007, Physical review. E, Statistical, nonlinear, and soft matter physics.

[30]  M. Perc.  Coherence resonance in a spatial prisoner's dilemma game , 2006 .

[31]  Martin A Nowak,et al.  Evolutionary games on cycles , 2006, Proceedings of the Royal Society B: Biological Sciences.

[32]  M. Nowak,et al.  Non-commercial Research and Educational Use including without Limitation Use in Instruction at Your Institution, Sending It to Specific Colleagues That You Know, and Providing a Copy to Your Institution's Administrator. All Other Uses, Reproduction and Distribution, including without Limitation Comm , 2022 .

[33]  M. Feldman,et al.  Local dispersal promotes biodiversity in a real-life game of rock–paper–scissors , 2002, Nature.

[34]  Josef Hofbauer,et al.  Evolutionary Games and Population Dynamics , 1998 .

[35]  Marcus Frean,et al.  Rock–scissors–paper and the survival of the weakest , 2001, Proceedings of the Royal Society of London. Series B: Biological Sciences.

[36]  H. Ohtsuki,et al.  Breaking the symmetry between interaction and replacement in evolutionary dynamics on graphs. , 2007, Physical review letters.

[37]  Arne Traulsen,et al.  Stochastic payoff evaluation increases the temperature of selection. , 2007, Journal of theoretical biology.

[38]  Marcus Frean.  The prisoner’s dilemma without synchrony , 1994, Proceedings of the Royal Society of London. Series B: Biological Sciences.

[39]  C. Hauert,et al.  Volunteering as Red Queen Mechanism for Cooperation in Public Goods Games , 2002, Science.

[40]  Heinz Mühlenbein,et al.  Evolution of Cooperation in a Spatial Prisoner's Dilemma , 2002, Adv. Complex Syst..

[41]  J. Gómez-Gardeñes,et al.  Robustness of cooperation in the evolutionary prisoner's dilemma on complex networks , 2007, q-bio/0703019.

[42]  F. C. Santos,et al.  Scale-free networks provide a unifying framework for the emergence of cooperation. , 2005, Physical review letters.

[43]  F. C. Santos,et al.  A new route to the evolution of cooperation , 2006, Journal of evolutionary biology.